Complex Analysis with Applications to Number Theory, Shorey Tarlok Nath

Автор: Thomas A. Garrity
Название: All the Math You Missed
ISBN: 1009009192 ISBN-13(EAN): 9781009009195
Издательство: Cambridge Academ
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Цена: 26400.00 T
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Описание: The second edition of this bestselling book provides an overview of the key topics in undergraduate mathematics, allowing beginning graduate students to fill in any gaps in their knowledge. With numerous examples, exercises and suggestions for further reading, it is a must-have for anyone looking to learn some serious mathematics quickly.

Автор: Kevin Broughan
Название: Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents
ISBN: 1107197120 ISBN-13(EAN): 9781107197121
Издательство: Cambridge Academ
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Цена: 155230.00 T
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Описание: This two-volume work presents the main known equivalents to the Riemann hypothesis, perhaps the most important problem in mathematics. Volume 2 covers equivalents with a strong analytic orientation and is supported by an extensive set of appendices.

Автор: Broughan Kevin
Название: Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic
ISBN: 110719704X ISBN-13(EAN): 9781107197046
Издательство: Cambridge Academ
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Цена: 128830.00 T
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Описание: This two-volume work presents the main known equivalents to the Riemann hypothesis, perhaps the most important problem in mathematics. Volume 1 presents classical and modern arithmetic equivalents, with some analytic methods. Accompanying software is freely available online.

Автор: Ablowitz, Mark J. (university Of Colorado Boulder) Fokas, Athanassios S. (university Of Cambridge)
Название: Introduction to complex variables and applications
ISBN: 1108959725 ISBN-13(EAN): 9781108959728
Издательство: Cambridge Academ
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Цена: 48570.00 T
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Описание: This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. It contains the essential topics along with advanced topics for use in challenging projects. Many worked examples, applications, and exercises are included.

Автор: Nikolai Nikolski
Название: Hardy Spaces
ISBN: 1107184541 ISBN-13(EAN): 9781107184541
Издательство: Cambridge Academ
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Цена: 61240.00 T
Наличие на складе: Невозможна поставка.
Описание: Designed for beginning graduate students, this book introduces and develops the classical results on Hardy spaces and applies them to fundamental problems in modern analysis. With solved exercises, short surveys of recent developments, and engaging accounts of the field`s main contributors, this book is the ideal source on Hardy spaces.

Автор: Shorey Tarlok Nath
Название: Complex Analysis with Applications to Number Theory
ISBN: 9811590966 ISBN-13(EAN): 9789811590962
Издательство: Springer
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Цена: 43780.00 T
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Описание: The book discusses major topics in complex analysis with applications to number theory. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two and three manifolds and number theory.

Автор: Hafedh Herichi, Michel L Lapidus
Название: Quantized Number Theory, Fractal Strings And The Riemann Hypothesis: From Spectral Operators To Phase Transitions And Universality
ISBN: 9813230797 ISBN-13(EAN): 9789813230798
Издательство: World Scientific Publishing
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Цена: 142560.00 T
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Описание: Studying the relationship between the geometry, arithmetic and spectra of fractals has been a subject of significant interest in contemporary mathematics. This book contributes to the literature on the subject in several different and new ways. In particular, the authors provide a rigorous and detailed study of the spectral operator, a map that sends the geometry of fractal strings onto their spectrum. To that effect, they use and develop methods from fractal geometry, functional analysis, complex analysis, operator theory, partial differential equations, analytic number theory and mathematical physics.Originally, M L Lapidus and M van Frankenhuijsen 'heuristically' introduced the spectral operator in their development of the theory of fractal strings and their complex dimensions, specifically in their reinterpretation of the earlier work of M L Lapidus and H Maier on inverse spectral problems for fractal strings and the Riemann hypothesis.One of the main themes of the book is to provide a rigorous framework within which the corresponding question 'Can one hear the shape of a fractal string?' or, equivalently, 'Can one obtain information about the geometry of a fractal string, given its spectrum?' can be further reformulated in terms of the invertibility or the quasi-invertibility of the spectral operator.The infinitesimal shift of the real line is first precisely defined as a differentiation operator on a family of suitably weighted Hilbert spaces of functions on the real line and indexed by a dimensional parameter c. Then, the spectral operator is defined via the functional calculus as a function of the infinitesimal shift. In this manner, it is viewed as a natural 'quantum' analog of the Riemann zeta function. More precisely, within this framework, the spectral operator is defined as the composite map of the Riemann zeta function with the infinitesimal shift, viewed as an unbounded normal operator acting on the above Hilbert space.It is shown that the quasi-invertibility of the spectral operator is intimately connected to the existence of critical zeros of the Riemann zeta function, leading to a new spectral and operator-theoretic reformulation of the Riemann hypothesis. Accordingly, the spectral operator is quasi-invertible for all values of the dimensional parameter c in the critical interval (0,1) (other than in the midfractal case when c =1/2) if and only if the Riemann hypothesis (RH) is true. A related, but seemingly quite different, reformulation of RH, due to the second author and referred to as an 'asymmetric criterion for RH', is also discussed in some detail: namely, the spectral operator is invertible for all values of c in the left-critical interval (0,1/2) if and only if RH is true.These spectral reformulations of RH also led to the discovery of several 'mathematical phase transitions' in this context, for the shape of the spectrum, the invertibility, the boundedness or the unboundedness of the spectral operator, and occurring either in the midfractal case or in the most fractal case when the underlying fractal dimension is equal to ? or 1, respectively. In particular, the midfractal dimension c=1/2 is playing the role of a critical parameter in quantum statistical physics and the theory of phase transitions and critical phenomena.Furthermore, the authors provide a 'quantum analog' of Voronin's classical theorem about the universality of the Riemann zeta function. Moreover, they obtain and study quantized counterparts of the Dirichlet series and of the Euler product for the Riemann zeta function, which are shown to converge (in a suitable sense) even inside the critical strip.For pedagogical reasons, most of the book is devoted to the study of the quantized Riemann zeta function. However, the results obtained in this monograph are expected to lead to a quantization of most classic arithmetic zeta functions, hence, further 'naturally quantizing' various aspects of analytic number theory and arithmetic geometry.The book should be accessible to experts and non-experts alike, including mathematics and physics graduate students and postdoctoral researchers, interested in fractal geometry, number theory, operator theory and functional analysis, differential equations, complex analysis, spectral theory, as well as mathematical and theoretical physics. Whenever necessary, suitable background about the different subjects involved is provided and the new work is placed in its proper historical context. Several appendices supplementing the main text are also included.

Автор: Travaglini
Название: Number Theory, Fourier Analysis and Geometric Discrepancy
ISBN: 1107044030 ISBN-13(EAN): 9781107044036
Издательство: Cambridge Academ
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Цена: 135170.00 T
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Описание: Geometric discrepancy theory is a rapidly growing modern field. This book provides a complete introduction to the topic with exposition based on classical number theory and Fourier analysis, but assuming no prior knowledge of either. Ideal as a guide to the subject for advanced undergraduate or beginning graduate students.

Автор: Ravi P. Agarwal; Kanishka Perera; Sandra Pinelas
Название: An Introduction to Complex Analysis
ISBN: 1489997164 ISBN-13(EAN): 9781489997166
Издательство: Springer
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Цена: 53100.00 T
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Описание: This senior undergraduate/graduate level textbook has been designed for an introductory course in complex analysis for students in the applied sciences. It follows the proof-theorem approach while presenting the material as 50 class-tested lectures.

Автор: Mathews, Mathews John H., Howell Russell W.
Название: Complex Analysis for Mathematics and Engineering
ISBN: 1449604455 ISBN-13(EAN): 9781449604455
Издательство: Jones & Bartlett
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Цена: 268140.00 T
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Описание: Intended for the undergraduate student majoring in mathematics, physics or engineering, the Sixth Edition of Complex Analysis for Mathematics and Engineering continues to provide a comprehensive, student-friendly presentation of this interesting area of mathematics. The authors strike a balance between the pure and applied aspects of the subject, and present concepts in a clear writing style that is appropriate for students at the junior/senior level.

Through its thorough, accessible presentation and numerous applications, the sixth edition of this classic text allows students to work through even the most difficult proofs with ease. New exercise sets help students test their understanding of the material at hand and assess their progress through the course. Additional Mathematica and Maple exercises are available on the publishers website.

Автор: Bengt Fornberg, Cecile Piret
Название: Complex Variables and Analytic Functions: An Illustrated Introduction
ISBN: 1611975972 ISBN-13(EAN): 9781611975970
Издательство: Mare Nostrum (Eurospan)
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Цена: 72730.00 T
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Описание: At almost all academic institutions worldwide, complex variables and analytic functions are utilized in courses on applied mathematics, physics, engineering, and other related subjects. For most students, formulas alone do not provide a sufficient introduction to this widely taught material, yet illustrations of functions are sparse in current books on the topic. This is the first primary introductory textbook on complex variables and analytic functions to make extensive use of functional illustrations. Aiming to reach undergraduate students entering the world of complex variables and analytic functions, this book utilizes graphics to visually build on familiar cases and illustrate how these same functions extend beyond the real axis. It covers several important topics that are omitted in nearly all recent texts, including techniques for analytic continuation and discussions of elliptic functions and of Wiener–Hopf methods. It also presents current advances in research, highlighting the subject’s active and fascinating frontier.The primary audience for this textbook is undergraduate students taking an introductory course on complex variables and analytic functions. It is also geared toward graduate students taking a second semester course on these topics, engineers and physicists who use complex variables in their work, and students and researchers at any level who want a reference book on the subject.

Автор: R. M. M. Mattheij
Название: Partial Differential Equations
ISBN: 0898715946 ISBN-13(EAN): 9780898715941
Издательство: Mare Nostrum (Eurospan)
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Цена: 142120.00 T
Наличие на складе: Нет в наличии.
Описание: Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component - modeling - to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters.